The Deputy First Minister told her party's Spring conference in Aberdeen that Scotland would be "in the removal business" immediately after a Yes vote in September.
Her words were seen as a clear indication the party would honour its pledge, set out in the independence White Paper Scotland's Future, to negotiate "the speediest safe removal" of Trident missiles from the Clyde, ideally by 2021.
Her comments, which drew loud applause from delegates at the Aberdeen Exhibition and Conference Centre, followed the revelation that the UK Government would not seek to extend Trident's stay as part of a wider independence settlement.
Ms Sturgeon said she had been proud to address an anti-nuclear weapons demonstration in Glasgow last week.
But she went on: "I'm fed up protesting against Trident. I want to see the back of Trident.
"In less than six months' time, if we vote Yes, we won't be in the protest business any more.
"We'll be in the removal business. After years of campaigning, we will have the power.
"And be in no doubt - we will use that power to remove Trident from Scotland once and for all."
She spoke out a day after David Mundell, the Scotland Office minister, said there was "no deal to be done on Trident" in the event of a Yes vote because of the Nationalists' staunch opposition.
Last month an unnamed Coalition Government minister said the UK might accept Alex Salmond's proposal for an independent Scotland to share the pound in a currency union in return for Trident remaining on the Clyde.
The suggestion was made despite clear denials by Chancellor George Osborne.
Ms Sturgeon described the UK's nuclear arsenal as "obscene and senseless" and a key reason "we must vote Yes".
Her comments came in a keynote address used primarily as a rallying cry to Nationalist activists with 159 days to go to the referendum.
In an often emotional speech, punctuated by frequent and rapturous applause from the 600 delegates in the hall, she quoted from the Eddi Reader song Wild Mountainside and its line: "The last mile is upon us. I'll carry you if you fall."
She told the conference: "After 80 years of campaigning, the last mile of our journey to independence is upon us. It may well be the hardest mile of all.
"So we will encourage each other, cheer each other and, yes, if needs be, we will carry each other over the finishing line.
"But, friends, we will not fail."
Twice in the course of her 36-minute speech - each time to thunderous cheers - she declared: "We are going to win."
She said: "The momentum is now clearly and firmly with Yes.
"Let me predict today that by the time we reach September, our momentum will be simply unstoppable."
Ms Sturgeon, who is the "Yes" minister in charge of the SNP's referendum strategy, hit out at former NATO head Lord Robertson's claim that independence would be "cataclysmic" for security in the West.
She also attacked Prime Minister David Cameron's refusal to face Mr Salmond in a head-to-head TV debate.
As expected, she reached out to Labour supporters, saying independence would allow them to "reclaim" their party
She announced a £5 million-a-year scheme to replace benefits for disabled people axed by the Coalition Government.
Commenting on behalf of the pro-UK Better Together campaign, West Dunbartonshire Labour MP Gemma Doyle said: "What we heard today from Nicola Sturgeon today was more of the same tired old tunes the nationalists have been signing for 80 years."